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Macaulay2Doc :: min(GradedModule)

min(GradedModule)

Synopsis

Description

i1 : R = QQ[a..e]

o1 = R

o1 : PolynomialRing
i2 : C = res coker vars R

      1      5      10      10      5      1
o2 = R  <-- R  <-- R   <-- R   <-- R  <-- R  <-- 0
                                                  
     0      1      2       3       4      5      6

o2 : ChainComplex
i3 : min C

o3 = 0
i4 : dual C
-- ker (45) called with OptionTable: OptionTable{SubringLimit => infinity}
-- ker (45) returned CacheFunction: -*a cache function*-
-- ker (45) called with Matrix: 0
--                            1
-- ker (45) returned Module: R
assert( ker(map(R^0,R^1,0)) === (R^1))
-- ker (46) called with OptionTable: OptionTable{SubringLimit => infinity}
-- ker (46) returned CacheFunction: -*a cache function*-
-- ker (46) called with Matrix: 0
--                            5
-- ker (46) returned Module: R
assert( ker(map(R^0,R^{{1}, {1}, {1}, {1}, {1}},0)) === (R^{{1}, {1}, {1}, {1}, {1}}))
-- ker (47) called with OptionTable: OptionTable{SubringLimit => infinity}
-- ker (47) returned CacheFunction: -*a cache function*-
-- ker (47) called with Matrix: 0
--                            10
-- ker (47) returned Module: R
assert( ker(map(R^0,R^{{2}, {2}, {2}, {2}, {2}, {2}, {2}, {2}, {2}, {2}},0)) === (R^{{2}, {2}, {2}, {2}, {2}, {2}, {2}, {2}, {2}, {2}}))
-- ker (48) called with OptionTable: OptionTable{SubringLimit => infinity}
-- ker (48) returned CacheFunction: -*a cache function*-
-- ker (48) called with Matrix: 0
--                            10
-- ker (48) returned Module: R
assert( ker(map(R^0,R^{{3}, {3}, {3}, {3}, {3}, {3}, {3}, {3}, {3}, {3}},0)) === (R^{{3}, {3}, {3}, {3}, {3}, {3}, {3}, {3}, {3}, {3}}))
-- ker (49) called with OptionTable: OptionTable{SubringLimit => infinity}
-- ker (49) returned CacheFunction: -*a cache function*-
-- ker (49) called with Matrix: 0
--                            5
-- ker (49) returned Module: R
assert( ker(map(R^0,R^{{4}, {4}, {4}, {4}, {4}},0)) === (R^{{4}, {4}, {4}, {4}, {4}}))
-- ker (50) called with OptionTable: OptionTable{SubringLimit => infinity}
-- ker (50) returned CacheFunction: -*a cache function*-
-- ker (50) called with Matrix: 0
--                            1
-- ker (50) returned Module: R
assert( ker(map(R^0,R^{{5}},0)) === (R^{{5}}))
-- ker (51) called with OptionTable: OptionTable{SubringLimit => infinity}
-- ker (51) returned CacheFunction: -*a cache function*-
-- ker (51) called with Matrix: 0
-- ker (51) returned Module: 0
assert( ker(map(R^0,R^0,0)) === (R^0))

             1      5      10      10      5      1
o4 = 0  <-- R  <-- R  <-- R   <-- R   <-- R  <-- R
                                                  
     -6     -5     -4     -3      -2      -1     0

o4 : ChainComplex
i5 : min dual C
-- ker (52) called with OptionTable: OptionTable{SubringLimit => infinity}
-- ker (52) returned CacheFunction: -*a cache function*-
-- ker (52) called with Matrix: 0
--                            1
-- ker (52) returned Module: R
assert( ker(map(R^0,R^1,0)) === (R^1))
-- ker (53) called with OptionTable: OptionTable{SubringLimit => infinity}
-- ker (53) returned CacheFunction: -*a cache function*-
-- ker (53) called with Matrix: 0
--                            5
-- ker (53) returned Module: R
assert( ker(map(R^0,R^{{1}, {1}, {1}, {1}, {1}},0)) === (R^{{1}, {1}, {1}, {1}, {1}}))
-- ker (54) called with OptionTable: OptionTable{SubringLimit => infinity}
-- ker (54) returned CacheFunction: -*a cache function*-
-- ker (54) called with Matrix: 0
--                            10
-- ker (54) returned Module: R
assert( ker(map(R^0,R^{{2}, {2}, {2}, {2}, {2}, {2}, {2}, {2}, {2}, {2}},0)) === (R^{{2}, {2}, {2}, {2}, {2}, {2}, {2}, {2}, {2}, {2}}))
-- ker (55) called with OptionTable: OptionTable{SubringLimit => infinity}
-- ker (55) returned CacheFunction: -*a cache function*-
-- ker (55) called with Matrix: 0
--                            10
-- ker (55) returned Module: R
assert( ker(map(R^0,R^{{3}, {3}, {3}, {3}, {3}, {3}, {3}, {3}, {3}, {3}},0)) === (R^{{3}, {3}, {3}, {3}, {3}, {3}, {3}, {3}, {3}, {3}}))
-- ker (56) called with OptionTable: OptionTable{SubringLimit => infinity}
-- ker (56) returned CacheFunction: -*a cache function*-
-- ker (56) called with Matrix: 0
--                            5
-- ker (56) returned Module: R
assert( ker(map(R^0,R^{{4}, {4}, {4}, {4}, {4}},0)) === (R^{{4}, {4}, {4}, {4}, {4}}))
-- ker (57) called with OptionTable: OptionTable{SubringLimit => infinity}
-- ker (57) returned CacheFunction: -*a cache function*-
-- ker (57) called with Matrix: 0
--                            1
-- ker (57) returned Module: R
assert( ker(map(R^0,R^{{5}},0)) === (R^{{5}}))
-- ker (58) called with OptionTable: OptionTable{SubringLimit => infinity}
-- ker (58) returned CacheFunction: -*a cache function*-
-- ker (58) called with Matrix: 0
-- ker (58) returned Module: 0
assert( ker(map(R^0,R^0,0)) === (R^0))

o5 = -6

See also